Can A Slow Shuttle Leave A Fast Ship Safely?

I am traveling in a Generational spaceship that has, over time, been accelerated to 0.4 light speed. The ship can not slow down until it nears its destination in 50 years. The ship has a small, conventionally powered shuttle craft whose top speed is 0.1 light speed. Can that shuttle leave the ship and maneuver about the ship without being left behind? I am thinking that when it leaves the ship it is moving at the same relative speed as the ship, and as long as it does not ever go below that speed, it can safely return.
The Space Shuttle orbiter Atlantis, framed by the California mountains, as it rides on the back of one of NASA's Boeing 747 Shuttle Carrier Aircraft (SCA) en route from California to the Kennedy Space Center, Florida. Image credit: NASA

The Space Shuttle orbiter Atlantis, framed by the California mountains, as it rides on the back of one of NASA's Boeing 747 Shuttle Carrier Aircraft (SCA) en route from California to the Kennedy Space Center, Florida. Image credit: NASA

It’s easier to get your head around this scenario if we start with a much simpler version of this, moving at much slower speeds...

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